Recently, the spin-averaged amplitudes for the two processes (REF ) were calculated in ref. [1]}. We have found complete agreement for all terms except for those containing \(\varepsilon _5\) . We have investigated the origin of this discrepancy. In the process of doing this we observed that we could reproduce the results of that reference if we do not flip the sign of \(\varepsilon _5\)  under permutations during the mapping of masters to pentagon functions as well as during the numerical crossing of momenta in order to obtain all other helicities. As explained above such a treatment of \(\varepsilon _5\)  is inconsistent. In order to verify this, we have calculated the terms of order \(\epsilon \)  and \(\epsilon ^2\)  of the one-loop pentagon integral which are sensitive to the treatment of the parity-odd invariant and functions. We have verified that the calculation in terms of pentagon functions as described above agrees with a direct numerical calculation of this integral with the program pySecDec [2]}. Our interpretation of the above result is that the disagreement between our calculation and ref. [1]} is due to an inconsistent treatment in ref. [1]} of \(\varepsilon _5\)  under permutations.
